Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥).

Front

What does the symbol '≤' indicate in an inequality?

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the appropriate region based on the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

How do you convert an inequality to slope-intercept form?

Back

To convert an inequality to slope-intercept form (y = mx + b), isolate y on one side of the inequality.

Front

What is the slope-intercept form of the inequality -10x + 2y > 14?

Back

The slope-intercept form is y > 5x + 7.

Front

What does it mean if an inequality has 'or equal to' in it?

Back

It means that the boundary line is included in the solution set, which is represented by a solid line when graphed.

Front

What is the first step in graphing the inequality y < -2x - 2?

Back

The first step is to graph the line y = -2x - 2 as a dashed line.

Front

How can you determine which side of the line to shade for the inequality y ≤ -2x - 2?

Back

Choose a test point (like (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side of the line that includes the test point.